After the restoration, why did the English government openly work to promote additional colonization in North America?

Colonization immediately after the Restoration was primarily a method by which Charles II could satisfy political and financial debts owed to those who helped to restore him to the throne. Some of those to whom he granted charters in America used them for financial gain; while others pursued more altruistic pursuits. Examples:

Admiral Penn had contributed financially to Charles' restoration. His son, William Penn inherited the debt. To satisfy the debt, Charles granted a large tract of land to Penn which Charles insisted be named "Penn's forest," in Latin, Pennsylvania.

A group of eight noblemen, including Anthony Ashley Cooper, the Earl of Shaftesbury, Edward Hyde, Earl of Clarendon, Sir George Berkeley, and George Monck, Earl of Albemarle, were awarded large tracts of land which was named Carolina, in honor of Charles' father, Charles I (Charles in Latin is Carolus.

The colonies so established became known as "Restoration Colonies" because of the role of their founders in the Restoration of Charles II to the throne.